Differentiated Shift Invariant Multivariate Integral Operators

George A. Anastassiou and Sorin G. Gal
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George A. Anastassiou: University of Memphis, Department of Mathematical Sciences
Sorin G. Gal: University of Oradea, Department of Mathematics

Chapter 13 in Approximation Theory, 2000, pp 347-372 from Springer

Abstract: Abstract This is a continuation of Chapter 11, among others, we still study global smoothness preservation over R d ,d > 1. Here are given sufficient conditions, so that the partial derivatives of general multivariate operators, examined in Chapter 11, enjoy most of the nice properties of their originals. Especially a sufficient condition is given so that the “global smoothness preservation” corresponding multivariate inequality is attained, that is sharp. Finally several applications are given, there the partial derivatives of very general specialized multivariate operators are shown to fulfill most of in Chapter 11 mentioned properties. In particular the partials of these operators are shown to preserve continuous multivariate probability density functions. Here we follow the basic study [20].

Keywords: Linear Operator; Partial Derivative; Probability Density Function; Probability Distribution Function; Nice Property (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1360-4_13

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DOI: 10.1007/978-1-4612-1360-4_13

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